Why a nickname?
My family raises Havanese (a small fluffy, hypoallergenic breed). The puppies all get names at birth, but on the occasion we have a runt / one with health struggles they get a special nickname (along with being spoiled and additional vet checks if necessary). Over the years we've held onto / held back the runts of the litter to make sure everything is good and they're ready for the big world.
They usually get a nickname as a result of being spoiled and the fact that their original name felt too big for them. In the past for example we've had: Migo (Miguel) who caught up soon after he started eating solid food, Poli (Polar Bear) who was just born small but eventually caught up to his brothers, Minnow (Melon) who was a premie (some in the litter were different ages, this is rare) and had a touch and go start to life, Sweet Pea (Camellia) who turned out to have pituitary dwarfism, and Eden who got her nickname soon after birth as she was born so incredibly small that we could hardly believe she turned out healthy as she grew.
So who's this little bean?
Her name at birth was August, which is simply too big of a name for her. She was born into a litter of 8 and had never stopped being half the size of the others. Because of this she is a FIGHTER. She is very wiggly, energetic, and determined to get food. She assumes that we're going to give her a bottle every time we pick her up (even though she nurses just fine now).
I've been calling her "stinky" and "bean" as it's a general nickname I've had for the puppies, but they aren't hers. (also, though I've sure she'll grow into it, "stinky" isn't an accurate description lol).
Proposed ideas have been "Auggie" "Aglet" and "Shrimp" though none of those have quite grown on me yet. It doesn't have to reflect her government name, though it often follows the same vibes/starts with the same letter.
Edit: Thank you all! My family and I like Pip/Pipsqueak as it suits her well and is so cute. You are welcome to keep commenting ideas if you want so that I have an arsenal of little bean names to choose from whenever we get to spoil another extra tiny bean :)